Team:IISER Bhopal/Model

iGEM IISER Bhopal

Modelling

The growth rate of our system may be modeled as a function of growth temperature and chaperons expressed, as governed by the Ratkowsky’s equation:


R(T,chap)= a * [(T - Tmin) * (1 - eb*(T - Tmax))]2


where, T : Temperature at which the culture is grown

Tmin : Minimum temperature below which growth is insignificant

Tmax: Limiting temperature above which growth is insignificant

a, b: Constants unique to the modified bacterial strain (reflects effect of TF)


For temperatures below that of optimum growth, the value of b is large (as b is a regression constant indicative of the decline of growth beyond the optimum temperature) therefore the second term within the bracket reduces to 1. Thus, the linear part of this equation can give a good estimate of the dependence of growth rates on temperatures which are below the optimum temperature. Hence, this may be simplified as:


√r = k (T - Tmin)


Hereon, the idea is to obtain growth curves of the system(both with and without the inserts) at different temperatures, so that we may plot the square root of growth rates as a linear function of temperature. Points obtained from the experiments are fitted into a linear equation, from which the slope and x-intercept are determined.

Fig.1: Ratkowsky root growth model for Cpn10/60 in pUC18 expressed in Rosetta cells at 18° C, 22° C, and 37° C.

Fig.2: Ratkowsky root growth model for TF (P.haloplanktis) in pUC18 expressed in Rosetta cells at 18° C, 22° C, and 37° C.

Fig.3: Ratkowsky root growth model for empty vector(pUC18) expressed in Rosetta cells at 18° C, 22° C, and 37° C.

Fig.4: Ratkowsky root growth model for Cpn60 in pUC18 expressed in Rosetta cells at 18° C, 22° C, and 37° C.


The x-intercept gives the lowest possible temperature at which growth occurs (the cell is still metabolically active). The R2 value indicates the goodness of the fit, and shows whether the regression is significant.

Results

System Tmin (° C) Goodness of fit R2 Standard Deviation
pUC18 9.5 0.7749 0.00985
Cpn60 -12 0.8425 0.00502
Cpn10/60 -5 0.997 0.000641
TF 8.9 0.999 0.000627

Interpretation

Systems without an insert (pUC18) show a Tminof 9.5° C. However, when the chaperons Cpn60 and Cpn10/60 were expressed, the Tmin were lowered to -12° C and -5° C respectively - which was as expected. TF also lowered the Tmin, albeit to a lesser extent. We also obtained a very low standard deviation for the TF and Cpn10/60 implying that the spread of points about the line was less, and thus the trend observed is significant. Standard deviation was slightly higher for empty vector and Cpn60, implying a wider distribution of data. Lower the R2 value obtained, higher is the goodness of fit.


References

  1. Ratkowsky, D. A., et al. "Model for bacterial culture growth rate throughout the entire biokinetic temperature range." Journal of bacteriology 154.3 (1983): 1222-1226.PMC217594
  2. Ferrer, Manuel, et al. "Chaperonins govern growth of Escherichia coli at low temperatures." Nature biotechnology21.11 (2003): 1266. doi: 10.1038/nbt1103-1266
  3. Team NCTU_Formosa